1. Technical Field
The present invention relates to a piezoelectric resonator element, a piezoelectric resonator, and an acceleration sensor that reduce sensitivity in other axis.
2. Related Art
In tuning fork type quartz crystal resonators, shapes of front and back faces (XY plane) of a resonating arm are commonly symmetrical. JP-A 2004-200917, for example, discloses a tuning fork type quartz crystal resonator including a resonating arm that has a recessed groove on its front and back faces. Tuning fork type quartz crystal resonators can be used as an acceleration sensor for detecting acceleration in Y-axis direction when a longitudinal direction of a resonating arm thereof is defined as Y-axis. In a case where the tuning fork type quartz crystal resonators perform accelerated motion toward +Z-axis direction that is a thickness direction of the resonators, the resonating arm of the resonators is affected by inertia force so as to bend in −Z-axis direction. On the other hand, in a case where the tuning fork type quartz crystal resonators perform accelerated motion toward −Z-axis direction, the resonating arm thereof bends in +Z-axis direction,
The inventor surveyed distribution of stress in a state that a resonating arm of a tuning fork type piezoelectric resonator composed of a Z-cut quartz crystal plate is bent, and found that the stress concentrates on a plane at +Z plane side. That is, the inventor found that a neutral plane that receives no compression and no tension by flexure is disproportionately formed at the +Z plane side. Accordingly, the rigidity at the +Z plane side of the tuning fork type quartz crystal resonator is higher than that at −Z plane side.
The tuning fork type quartz crystal resonator is mainly composed of the Z-cut quartz crystal plate as described above. In this case, the bonding state of crystal in the thickness direction is asymmetric, whereby the resonator has anisotropy in the thickness direction. That is, in a case where the tuning fork type quartz crystal resonator is turned over, an alignment of crystal of the resonator is not same as that before the turning over of the resonator. It is considerable that an elastic constant, a piezoelectric constant, and the like that relate to bending stress on the +Z plane are not same as those on the −Z plane due to the anisotropy so as to generate difference of rigidity, whereby the rigidity at the +Z plane side is higher in a case of quartz crystal.
In a case where the tuning fork type quartz crystal resonator in which the rigidity at the +Z plane side is different from that at the −Z plane side is used as an acceleration sensor for detecting acceleration in Y-axis direction, the acceleration sensor responds to acceleration in Z-axis direction, that is, the sensitivity in other axis is generated. Therefore, an accurate detecting result of acceleration in Y-axis direction can not be obtained.
It is considerable that such problem of the sensitivity in other axis occurs as follows. In a case where the rigidity at the +Z plane side with respect to flexure in Z-axis direction and that at the −Z plane side are unbalanced, if the tuning fork type quartz crystal resonator is excited so as to be allowed to perform flexural vibration, the +Z plane side from the neutral plane described above has strong rigidity with respect to the flexural vibration and the −Z plane side has weak rigidity. As a result, amplitude of vibration at the −Z plane side becomes larger than that at the +Z plane side. Therefore, the resonating arm is drawn toward the +Z plane side due to tensile stress from the +Z plane that has large rigidity at a part where the amplitude of vibration is large. Accordingly, the resonating arm does not vibrate horizontally to a plane formed by the tuning fork type quartz crystal resonator having a plate shape as a whole. That is, the resonating arm of the tuning fork type quartz crystal resonator vibrates not only in X-axis direction but also in Z-axis direction. In a case where the tuning fork type quartz crystal resonator performs accelerated motion under such vibrating state, a vibrating component in Z-axis direction of the resonating arm receives inertia force due to the acceleration in Z-axis direction, whereby a vibrating frequency in Z-axis direction varies. In accordance with the variation of the vibrating frequency in Z-axis direction, the resonance frequency of the resonating arm vibrating in X-axis direction varies. Then, this effect appears as a noise together with a desired resonance frequency of the tuning fork type quartz crystal resonator.